Method of Computing Global-to-Local Metrics for Recognition

ABSTRACT

A method of computing global-to-local metrics for recognition. Based on training examples with feature representations, the method automatically computes a local metric that varies over the space of feature representations to optimize discrimination and the performance of recognition systems. 
     Given a set of points in an arbitrary features space, local metrics are learned in a hierarchical manner that give low distances between points of same class and high distances between points of different classes. Rather than considering a global metric, a class-based metric or a point-based metric, the proposed invention applies successive clustering to the data and associates a metric to each one of the clusters.

BACKGROUND OF THE INVENTION

The classification problem can be formulated as a verification schemewhere the objective is to determine if a pair of points is positive ornegative, i.e. positive if the points belong to the same class, negativeotherwise. Given a set of labeled data, one can try to learn the metricthat gives a discriminative distance in a given feature space that wouldperform the best for this task; which is to give a low distance betweenpoints of a positive pair and a high distance to points of a negativepairs. A detailed overview of this type of methods can be found in [1].

Global metric learning has become popular to improve classificationalgorithms, such as the K-nearest neighbors (KNN) classificationalgorithm [2]. It often consists of estimating the optimal covariancematrix of the Mahanlobis distance that will be used for classification.While these kinds of global metrics have shown impressive improvementsfor classification, they do not capture local properties in the featurespace which may be relevant for complex data distributions. To overcomethis difficulty, a two step approach is generally employed [3, 4].Firstly, a global metric is learned and training points in the featurespace are transformed accordingly; secondly, a local metric is estimatedin the neighborhood of each transformed training point. These localmetrics allow for better adaptiveness to the data but often require anheuristic choice of locality.

The proposed invention is instead a hierarchical global-to-localapproach, where the metric is iteratively refined and learned using thedata distribution Itself. The approach starts by estimating a globalmetric and applying the corresponding (metric) transformation to thedata. Then the transformed points are clustered to obtain a set of Kclusters. These two steps are recursively applied to each cluster untila termination criterion is satisfied on the cluster. such criteria canbe e.g. maximal height in the tree, minimal variance of the data pointsin the cluster or a minimum number of data points in the cluster. Thisforms a tree with a metric associated to each node.

DETAILED DESCRIPTION

Below follows a detailed description of the invention.

Given a set of labeled points {x_(i), i=1 . . . N}, we successivelyapply a global metric learning algorithm on sets of hierarchicallyclustered points. This has the effect of forming a metric tree. Forsimplicity of presentation, we assume the number of clusters for eachinstance of the clustering algorithm to be constant and equal to K. Letn_(i,j), be the j^(th) cluster at level i and A_(i,j) be the associatedmetric transformation matrix. The metric is learned on the set oftransformed points {y_(i,j)=π_(k=0) ^(i−1)A_(i−1,j)/Kx_(i,j)}, e.g.using, but not restricted to, the Information Theoretic Metric Learningalgorithm (ITML) proposed in [5].

Before applying the clustering algorithm to a node n_(i,j), we apply thetransformation associated to the metric of that to node the points givenby its parents nodes.

We can now use our metric tree to evaluate the distance between any twodata points, e.g. image descriptors, face feature vectors or otherfeature representations. First, each point is injected in the tree andits path is recovered. In particular, we identify the last node of thetree that contain both points. The distance between the points is thenthe one obtained using the metric associated to this node, possiblycompounded with the metrics of parent nodes.

In the worst case, the last common node is the root of the tree, andtherefore, the distance will use the global metric. The deeper in thetree the common node is, the more local the metric is. Compared to purelocal or global methods, this approach has the advantage of refining themetric in dense or complex areas, according to the termination criterion(e.g. maximum leaf size, maximum leaf variance, maximum height limit).

A possible issue with this formulation is the high dependence on theclustering boundary. Points can be close to each other and separatedquite early in the clustering tree. To reduce the influence of thisdecision, it is possible to construct multiple metric trees and averagethe distances given by each one of them.

In a preferred embodiment of the invention, a method for global-to-localmetric learning is presented, the method comprising the steps of;

-   -   learning a metric tree (as may be illustrated as in FIG. 1),    -   classifying or comparing test data using this metric tree.

In another embodiment of the present invention, a computer programstored in a computer readable storage medium and executed in acomputational unit for global-to-local metric learning comprising thesteps of; learning a metric tree, classifying or comparing test pointsusing this metric tree.

Yet another embodiment of the present invention, a system forglobal-to-local metric learning and classification containing a computerprogram for global-to-local metric learning comprising the steps of;

-   -   learning a metric tree,    -   classifying or comparing test data using this metric tree.

In another embodiment of the present invention a system or device isused for obtaining images, analyzing, and responding to results fromclassification using a global-to-local metric, as may be seen in FIG. 2.Such a system may include at least one Image acquisition device 101 anda computational device 100.

We have described the underlying method used for the present inventiontogether with a list of embodiments. Possible application areas for theabove described invention range from, but are not restricted to, objectrecognition and face recognition to classification of image content.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic layout of a global-to-local metric tree.

FIG. 2 illustrates systems comprising of a camera and computational unitusing the global-to-local metric.

REFERENCES

[1] D. Ramanan, S. Baker. “Local Distance Functions: A Taxonomy, NewAlgorithms, and an Evaluation” International Conference on ComputerVision (ICCV) Kyoto, Japan, September 2009.

[2] K. Weinberger, J. Blitzer, L. Saul. “Distance Metric Learning forLarge Margin Nearest Neighbor Classification”Advances in NeuralInformation Processing Systems 18, MIT Press, Cambridge, Mass., pp.1473-1480, 2006.

[3] C. Domeniconi and J. Peng and D. Gunopulos, “Locally Adaptive MetricNearest Neighbor Classification” IEEE Transactions on Pattern Analysisand Machine Intelligence, vol. 24, pp. 1281-1285, 2002.

[4] T. Hastie, R. Tibshirani, “Discriminant Adaptive Nearest NeighborClassification,” IEEE Transactions on Pattern Analysis and MachineIntelligence, vol. 18, no. 6, pp. 607-616, June, 1996.

[5] J. V. Davis, B. Kulis, P. Jain, S. Sra, and I. S. Dhillon.“Information-theoretic metric learning” In Proceedings of the 24thinternational Conference on Machine Learning, Corvalls, Oreg., Jun.20-24, 2007.

1. A method for global-to-local metric learning for classification andrecognition comprising the steps of; using a tree structure constructedwith a clustering algorithm at each level, and associating a metric toeach one of the tree nodes.
 2. The method according to claim 1, whereinsaid clustering algorithm is the K-means clustering.
 3. The methodaccording to claim 1 wherein said metric is a symmetric matrix obtainedwith the ITML algorithm.
 4. The method according to claim 1 wherein saidclustering algorithm uses the local metric at each node.
 5. A computerprogram stored in a computer readable storage medium and executed in acomputational unit for global-to-local metric learning according toclaim
 1. 6. A computer program according to claim 5, further comprisingthe steps of; finding a relevant local metric for a given featurecomparison, and; using this local metric for classification orrecognition.
 7. A system for recognition comprising of a computerprogram according to claim 5 further using feature representations whichare compared with a method according to claim
 6. 8. A system accordingto claim 7 where the feature representations represent objects inimages.
 9. A system according to claim 8 where the objects are faces.